Nassif arrived in court on Wednesday with a letter from the Department of Children and Family Services saying that the abuse claim was "unfounded." A judge granted him two monitored visits with the kids before a scheduled hearing on Oct. 9, where custody will be discussed further.

"He is delighted and continues to hope that the children will be able to spend significant time with both parents and grow up and experience as normal a childhood as they can," a source close to Nassif tells PEOPLE. Nassif has scheduled visits with his kids on Sept. 29 and Oct. 6.

Maloof, meanwhile, is "comfortable with the court's decision," her rep Howard Bragman tells PEOPLE. "She respects it. She is happy that the kids are spending monitored time with their father."